Solution to Poisson Boltzmann Equation in Semi-Infinite and Cylindrical Geometries

Linearized Poisson-Boltzmann equation (PBE) gives us simple expressions for charge density distribution (ρe) within fluids or plasma. A recent work of this author shows that the old boundary conditions (BC), which are usually used to solve PBE, have serious defects. The old solutions turned out to be non-unique, and violates charge conservation principle in some cases. There we also derived the correct formula of ρe for a finite, rectangular geometry, using appropriate BCs.
Here we consider some other types of geometries and obtain formula of ρe, which may be useful to analyse different experimental conditions.
Category:Condensed Matter

Phonons are 'Bosonic' Particles

A team of researchers working at Osaka University in Japan has devised an experiment that gave results showing that phonons mix in such a way that they can be now be classified as 'bosonic' particles. Dave Kielpinski with Hewlett Packard Laboratories, offers a News & Views piece on the work done by the team and explains how it relates to work done with photons and other quantum particles. [12]
Solitons are localized wave disturbances that propagate without changing shape, a result of a nonlinear interaction that compensates for wave packet dispersion. Individual solitons may collide, but a defining feature is that they pass through one another and emerge from the collision unaltered in shape, amplitude, or velocity, but with a new trajectory reflecting a discontinuous jump.
Working with colleagues at the Harvard-MIT Center for Ultracold Atoms, a group led by Harvard Professor of Physics Mikhail Lukin and MIT Professor of Physics Vladan Vuletic have managed to coax photons into binding together to form molecules – a state of matter that, until recently, had been purely theoretical. The work is described in a September 25 paper in Nature.
New ideas for interactions and particles: This paper examines the possibility to origin the Spontaneously Broken Symmetries from the Planck Distribution Law. This way we get a Unification of the Strong, Electromagnetic, and Weak Interactions from the interference occurrences of oscillators. Understanding that the relativistic mass change is the result of the magnetic induction we arrive to the conclusion that the Gravitational Force is also based on the electromagnetic forces, getting a Unified Relativistic Quantum Theory of all 4 Interactions.
Category:Condensed Matter

Authors:Swapnil PatilComments: Total 16 pages. The replacement elaborates the supplementary information of our previous version and refines the language of presentation. Many of our ideas should become very clear after reading this version (also published as arXiv:1409.7156v5).

We critically examine the non-Fermi liquid (NFL) behavior observed in heavy fermion systems located close to a magnetic instability and suggest a conceptual advance in physics in order to explain its origin. We argue that the treatment of electronic states responsible for magnetism near the Quantum Critical Point (QCP), should not be accomplished within the quantum mechanical formalism; instead they should be treated semi-classically. The observed NFL behavior can be explained within such a scenario. As a sequel we attempt to discuss its consequences for the explanation of high-TC superconductivity observed in Cuprates.
Category:Condensed Matter

Can CDW Physics Explain Ultra Fast Transitions, and Current Vs. Applied Electric Field Values Seen in the Laboratory?

The tunneling Hamiltonian is a proven method to treat particle tunneling between different states represented as wavefunctions in many-body physics. Our problem is how to apply a wave functional formulation of tunneling Hamiltonians to a driven sine-Gordon system. We apply a generalization of the tunneling Hamiltonian to charge density wave (CDW) transport problems in which we consider tunneling between states that are wavefunctionals of a scalar quantum field. We present derived I-E curves that match Zenier curves used to fit data experimentally with wave-functionals congruent with the false vacuum hypothesis. The open question is whether the coefficients picked in both the wave-functionals and the magnitude of the coefficients of the driven sine Gordon physical system should be picked by topological charge arguments that in principle appear to assign values that have a tie in with the false vacuum hypothesis first presented by Sidney Coleman. Our supposition is that indeed this is useful and that the topological arguments give evidence as to a first order phase transition which gives credence to the observed and calculated I-E curve as evidence
Category:Condensed Matter